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Seneca, Ad Lucilium Epistulae Morales, 58.31, on Plato's lifespan:

Nam hoc scis, puto, Platoni diligentiae suae beneficio contigisse, quod natali suo decessit et annum unum atque octogensimum inplevit sine ulla deductione. Ideo magi, qui forte Athenis erant, inmolaverunt defuncto, amplioris fuisse sortis quam humanae rati, quia consummasset perfectissimum numerum, quem novem novies multiplicata conponunt.

Translation:

For I suppose you know that thanks to his careful management, Plato completed eighty-one years of life and died on his birthday, not a day short. For that reason, some Persian soothsayers who happened to be in Athens made burnt offerings to him after his death, believing that since he had completed the most perfect number (which they get by multiplying nine times nine), his fate was of more than humankind.

I can't understand the literal meaning of the sentence amplioris fuisse sortis quam humanae rati, especially the phrase humanae rati. Also I wonder why he used fuisse, instead of a participle.

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I think the key here is first to match the participle (really verb in deponent) rati to its subject.

rati cannot be related to humanae (which is also an adjective) as the case and/or the number/gender do not match. We have no other choice here but to attach rati to magi. (i.e., "The soothsayers believing ...)

Now, Like other verbs of thinking such as cogito, reor can be attached with "object clause", i.e., acc+inf construction. (as in English "I think him to be nice"). Or, as we have here: "reor [eum] esse x".

Here we also have the genitive of quality ("being of"), in the expression esse amplioris sortis quam humanae.

All this can be literally translated:

The soothsayers believed [him] to be of more distinguished rank than (mere) human [rank].

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    I agree with this analysis; I would add that (a) since reri means “believe,” the perfect tense may raise our eyebrows, but in reality that is a very frequent construction (probably stemming from the original meaning, which is more akin to “reckon, judge, conclude”), whereas the present participle seems to be basically non-existent; and (b) I think “fate” is a really strange translation here; what is meant is “rank” or “sort.”
    – Sebastian Koppehel
    Commented Dec 16, 2022 at 21:18
  • @SebastianKoppehel, thanks. I modified the translation.
    – d_e
    Commented Dec 16, 2022 at 21:46
  • @d_e: In Seneca's first sentence he is speaking to a second person about Plato, hence indirect speech, "(eum) contigisse". The same sentence continues with Plato's behaviour, "decessit" & "inplevit", written directly. Shouldn't it be all direct or all indirect; Seneca is still talking to this second person?
    – tony
    Commented Dec 22, 2022 at 12:37
  • @tony, it might be that he says that the lister knew of Plato; but then go on adding details he did not think the listener knows.
    – d_e
    Commented Dec 22, 2022 at 14:35

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